Rigid-body rotation worksheet with answers

Free printable Rigid-body rotation worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
R = 0.7 mn = 1800 rpm40 kg

A flywheel is a uniform solid disc of mass 40 kg and radius 0.7 m. It spins at 1800 rpm. Find its kinetic energy Ek in kJ.

M = 40 kgR = 0.7 mn = 1800 rpm
Ek = kJ
2.Easy
Or = 0.1 mL = 1.4 m1.5 m5 kg4.5 kg

A pendulum is made of a uniform slender rod (5 kg, 1.4 m long) pivoted at its top end O, with a solid sphere of mass 4.5 kg and radius 0.1 m fixed to its lower end. The centre of the sphere is 1.5 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 5 kgL = 1.4 mmsphere = 4.5 kgr = 0.1 md = 1.5 m
IO = kg·m²
3.Medium
L = 3 mm = 13.5 kgα

A uniform slender rod of mass 13.5 kg and length 3 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration atip of the free end just after release.

m = 13.5 kgL = 3 mg = 9.81 m/s²
atip = m/s²
4.Medium
L = 2.3 mm = 19.5 kgα

A uniform slender rod of mass 19.5 kg and length 2.3 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find its angular acceleration α just after release.

m = 19.5 kgL = 2.3 mg = 9.81 m/s²
α = rad/s²
5.Hard
θ = 15°vs = 2 m

A thin hoop starts from rest and rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 2 m along the slope.

θ = 15°s = 2 mI = m·r²g = 9.81 m/s²
v = m/s
6.Hard
disc: 2 kgring: 14 kgn1​ = 900 rpm

A uniform solid disc (mass 2 kg, radius 0.5 m) spins freely at 900 rpm about a vertical frictionless shaft. A thin ring of mass 14 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. Find their common speed n2 in rpm.

Mdisc = 2 kgMring = 14 kgR = 0.5 mn1 = 900 rpm
n2 = rpm

Answer key

  1. 1. Ek = 174.1 kJ
  2. 2. IO = 13.41 kg·m²
  3. 3. atip = 14.71 m/s²
  4. 4. α = 6.398 rad/s²
  5. 5. v = 2.253 m/s
  6. 6. n2 = 60 rpm

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